Prediction of rock mass mechanical properties from acoustic wave velocity using a Hoek-Brown constrained Component-Parameter model

Abstract

Acoustic testing of rock masses is a widely used technique for the rapid evaluation of rock masses in engineering investigations, with key applications in tunnelling, slope stability management and related projects. However, conventional acoustic wave testing methods only provide qualitative insights into the mechanical properties of rock masses, necessitating Supplemental laboratory or in-situ mechanical tests to obtain quantitative values for critical parameters such as the elastic modulus and internal friction angle. This dual-testing requirement significantly hampers both efficiency and timely decision-making in the field. To overcome these limitations, this study conducted a series of laboratory and field experiments. A modified Wyllie equation was applied to analyze the relationships among rock porosity, mineral composition, and acoustic wave velocity. Polynomial regression modeling was then used to quantify the effects of pore space and mineral components on mechanical parameters, leading to the construction of a Hoek–Brown–constrained component-parameter correlation model. This approach identified the sensitivity response mechanism between acoustic wave characteristics and mechanical parameters. The results demonstrate that the model effectively predicts shear-strength indices (internal friction angle, R² = 0.93–0.94, cohesion, R² = 0.97–0.98) and deformation parameters (elastic modulus, R² = 0.94–0.95) for representative rock masses. Specifically, the internal friction angle (φ) was found to be the most sensitive parameter to acoustic wave variations (sensitivity coefficient ∼ 10^-5), followed by cohesion (c, ∼10^-6 to 10^-5) and elastic modulus (E, ∼10^-8 to 10^-7). Among them, internal friction angle exhibits the highest sensitivity to acoustic measurements, followed by cohesion, indicating strong potential for quantitative field application. Validation using metrics like Mean Squared Error (MSE = 0.001 ∼ 0.097) and Root Mean Squared Error (RMSE = 0.032 ∼ 0.311) confirmed the model’s high predictive accuracy and robustness beyond R2. The acoustic-mechanical correlation model proposed in this study provides a new approach for rapid rock mass assessment and dynamic decision-making in tunnel support design, slope stability assessment, and other geotechnical engineering practices. It also presents a novel framework for comprehensively evaluating multiple parameters in rock mass engineering applications.